Question

Regression:  

Examine the relationship between the number of units produced and the number of production batches and their effect on total manufacturing overhead.

a. What is the coefficient of determination?

b. How did multiple (versus single) regression help/hurt the r-squared?

Sales Price Per Unit $400.00 Variable Selling and General Expenses per unit Monthly Fixed Selling and General Expenses $12.00 $ 2,000 DirectDirect Manufacturin Machine MaterialLabor Number of Production Units Batches Produced Overheadi n Numbe Month Jan Feb 3 Mar Year 2,001 2,001 2,001 2,001 2,001 2,001 2,001 2,001 2,001 2,001 2,001 2,001 Hours 10,991 |1,5573,703 4,646 9,7241,2593,0594,408 9,830 970 2,411 3,674 11,0061,6313,653 4,723 10,4131,232,850 4,028 10,403 1,3912,970 4,280 11,3071,4793,750 5,750 9,7169552,060 2,530 10,3101,808 3,822 4,992 9,622988 2,4483,520 10,2371,483 3,683 4,613 11,1201,5973,802 5,530 10,3111,7153,630 4,453 10,1039512,173 3,039 10,7771,507 3,587 4,197 9,8224731,0501,330 10,5271,493 3,480 4,083 9,3315781,2942,006 10,697882,087 2,698 9,7677711,7272,440 10,2416921,697 2,419 9,6959402,1463,066 10,7461,498 3,802 5,171 10,7901,6153,420 4,697 121 103 5 May 10 95 Jul Aug Sep Nov 124 12 10 Jan Feb Mar 121 71 14 15 16 17 10 35 May 116 Jul Aug Sep 19 71 57 20 10 73 23 24 Nov 114 68,304 92,293 Manufacturing Overhead y- 13.088x + 9064.8 R2 0.5264 11,000 10,500 10,000 9,500 9,000 8,500 8,000

Answer 1

Kindly refer ot the solution attached below.

Number of Observation production Units Manufacturing produced overhead SUMMARY OUTPUT Production batches and unit produced) batches 121 103 82 123 95 100 125 10991 9724 9830 11006 10413 10403 11307 9716 10310 9622 10237 11120 10311 10103 10777 9822 10527 9331 10697 9767 10241 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.22997 0.052886 0.009835 29.94063 24 10 130 ANOVA 10 df MS F gnificance F 124 128 121 71 122 35 116 Regression Residual Total 1 1101.246 1101.2461.228463 0.279676 22 19721.71 896.4415 23 20822.96 12 13 14 15 16 17 18 19 20 21 10 coefficientsandard Err( t Stat P-value Lower 95%Upper 95%ower 95.0%pper 95.0% 10 4 114.702 18.54846 6.18391 3.18Е-06 76.23487 153.1692 76.23487 153.1692 Intercept Number of production batches -2.80632 2.531953 -1.10836 0.279676-8.05727 2.444632 -8.05727 2.444632 p value of production batches is >5 % hence the relationship between the units 71 57 56 producted and prduction batches is NOT significent. 10

21 10 56 10241 73 9695 SUMMARY OUTPUT(Manufacturinf overhead Vs Production batches and unit produced) 128 114 10746 23 24 10790 6 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.936056 0.8762 0.86441 199.8574 24 ANOVA sS MS gnificance F Regression Residual Total 2 5936671 2968336 74.31434 2.98E-10 21 838802.5 39942.98 23 6775474 Coefficientsandard Err t Stat p-value Lower 95%Upper 95% ower 95.091 pper 95.0% 5.62E-21 7473.212 8325.357 7473.212 8325.357 Number of production batches 133.7729 17.36656 7.702902 1.5E-07 97.65716 169.8886 97.65716 169.8886 15.6086 1.423141 10.96771 3.75E-10 12.64902 18.56819 12.64902 18.56819 ntercept 7899.284 204.8807 38.55554 Units produced p value of all independent paramenters is 5 % hence the relationship between the Manufacturing overhead vs units producted and prduction batches is significen and is given by Y(man ovrhead) 7899.3+133.8(production batches)+15.6(units produced)

As explained, there is NO relationship /corellation betwene the variable number of units and batches .

However vis a vis manufacturing overhead ,both variables are related as shown by the equation.

Y(man ovrhead)=7899.3+133.8(production batches)+15.6(units produced)

The coefficient of variables is given by

	Coefficients
Intercept	7899.284343
Number of production batches	133.772892
Units produced	15.60860328

	Coefficients
Intercept	7899.284343
Number of production batches	133.772892
Units produced	15.60860328

Now to the R²

It is the percentage of the response variable variation that is explained by a linear model.

The value of R squared is also called as the coefficent of determination .

In first case ( regression between unit and batches) the coefficient of determination is 0.053 (5.3%) while it increases phenomenally to 0.876 (87.6%) when we did the multiple regression to ascetain relationship of more than one independent variable to the dependent variable.

We say that a

• Only 5.3% of the model variability of the response data around its mean is explained in first case
• 87.6% of the model variablity isof the response data around its mean is explianed.